Questions tagged [finite-automata]
Questions about finite automata, an elementary automaton model with finite memory. It is equivalent to regular languages and the basis for many more complex models.
216
questions with no upvoted or accepted answers
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Make a tag system simulate a finite automaton?
Tag systems are Turing-complete. I was wondering if there is any easy way to create tag systems that simulate finite automata. So create tag systems that recognize languages, e.g. by having at the end ...
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1
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A Turing machine with each cell accessed at most $10$ times has an equivalent NFA
I am confused by the following claim:
Let $T$ be a (decider, single-tape) Turing machine with the property that for every input, every cell on its tape is accessed at most $10$ times. Then there is a ...
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315
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Why does Non Determinism not enhance FA like it does for PDA
Both Deterministic and Non deterministic Finite Automata can recognize the same universe of regular languages. On the other hand, Deterministic Push Down Automata can only recognize a subset of ...
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Languages recognized by finite state automata of polynomially growing size
In the course of my research (condensed matter physics stuff), I stumbled over the following concept:
The class of regular languages can be defined via finite state machines (FSM):
A language $L$ is ...
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4
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Inverse operation to concatenation for regular languages
I'm currently in need of the inverse operation of the concatenation of 2 regular languages.
Formally, for 3 regular languages $A,B,C$ such that $A \cdot B = C$, only $A$ and $C$ are known, and $B$ is ...
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4
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Simultaneous reachability of NFA states
Suppose I have a $n$-state non-deterministic finite automaton $F$ over alphabet $\Sigma$. Let $S(x)$ be the set of states reachable from the starting state by consuming string $x$.
I am interested for ...
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Does Brzozowsky's algorithm always produce the right minimum DFA?
Let's say I have this NFA automaton A:
...
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4
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107
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Quality of Reduction of finite automata using different congruences
I am looking for an example, which corresponds to what I've learned in my Applied Automata Theory Class:
Given a NFA $\mathcal{A}$,
a $\approx _\mathcal{A}$ quotient automaton can be bigger then a $...
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3
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1
answer
181
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NP completeness of deciding whether a set of examples, consisting of strings and states, has a corresponding DFA?
I'm working on a textbook problem, 7.36 in Sipser 3rd edition. It claims that if we are given an integer $N$ and set of pairs $(s_i, q_i)$, where $s_i$ are binary strings and $q_i$ are states (we are ...
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Minimal regular expression from minimal NFA for finite language in polynomial time?
Given a minimal NFA for a finite language, is there a polynomial-time algorithm to find a minimal regular expression for the same language?
This question is based on a recent question regarding ...
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Tree Automata Operators
I am trying to understand the Projection operation (linear tree homomorphism) and Cylindrification operation (inverse tree homomorphism) from the book. Linear Tree homomorphism is defined as follows:
...
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NFA random generator
I'm working on a NFA to DFA conversion tool that is different from the Subset Construction and I need to test this tool.
In order to be sure that the immplementation has no bug I'd like to generate a ...
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Let $∑$ be an alphabet. Is the set of all DFAs over $∑$ countable?
Let $∑$ be an alphabet. Is the set of all DFAs over $∑$ countable?
I know the set of all regular languages is countable, however, it is impossible to build an injection from the DFAs to the regular ...
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What extension of a finite-state machine is modeled by aliasing inputs?
Recently, I’ve been interested in the console of the Source game engine, more specifically, its alias command, which allows one command to invoke others. It may ...
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Translating weighted regular expressions with the complement operator to weighted deterministic automata
I want to implement regexp search via translation to deterministic automata, as a toy project.
TLDR: how to combine the extended regular expressions with the weighted regular expressions, with the ...
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How to build a minimal string matching DFA with limited memory?
I am working on finite state machine pruning, a problem that requires me to build finite state machines (in the manner of the Aho Corasic algorithm) to match an evolving input string against a set of ...
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closure property violated by palindrome language
It is well established that palindrome language is non-regular. The one way to prove it is by means of pumping lemma. The other way is violating the closure properties of regular language. The ...
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Regular string relations - proof of correctness
Let $T \subseteq \Sigma^* \times \Sigma^*$ be a regular (rational) relation. We define the obligatory rewrite relation over $T$ as follows:
$$
R^{obl}(T) := N(T) \cdot (T \cdot N(T))^*
$$
$$
N(T) := ...
2
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can a DFA with only final states be minimized?
I need to construct a DFA for a certain language with as little states as possible.
so far my "best" solution contains 15 states. however, people claim it is doable in 7 states only. I tried for ...
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Which of these languages is regular? The Pumping Lemma seems to show none are
I've been reviewing past paper questions for an automaton course, and came across a question which effectively asks, which of these languages is regular?
$$
\{\ 0^m1^{(m \times n)}0^n\ \colon\ m,n\ge ...
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Why are VFSMs not more commonly used?
For a job several years ago I worked with a team using technologies built around Virtual Finite State Machine models for system fault analysis and remediation. Since then, I've found it to be a ...
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121
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Intersection of two deterministic parity automata
Given two deterministic parity automata $A_1=(Q_1,\Sigma,\delta,q_{01},c_1)$ and $A_2=(Q_2,\Sigma,\delta,q_{02},c_2)$ with the finite set of states $Q_i$, the finite alphabet $\Sigma_i$, the ...
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Extending Thompson's NFA algorithm with backreferences
I'm looking for an algorithm as efficient as possible for a regex engine that supports submatch tracking (a.k.a capturing parentheses) and backreferences. What I mean by as efficient as possible is ...
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2
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658
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Number of non deterministic finite automata that can be constructed for $n$ states and alphabet with $m$ symbols
I came across the fact that
The number of DFAs that can be constructed for $n$ number of states and alphabet containing $m$ symbols is $n\times (\color{red}{n}^m)^n \times 2^n$
So I was wondering ...
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2
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Minimization of simple cyclic automata
Version 1 of the question: I am looking for any correct $O(n)$ algorithm in the literature which will solve the DFA minimization problem referred to in the quote below from [Almeida & Zeitoun 2008]...
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State of the Art in linear-time DFA minimization
What is the most complicated kind of deterministic finite-state automaton that can be minimized in $O(n)$ time?
Here’s what I’ve been able to find so far:
The acyclic case has been solved. So any ...
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2
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0
answers
360
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Powerset construction of minimal NFA will result into minimal DFA?
I was just thinking about the powerset construction and it is clear to me that the powerset construction will result into a DFA $D$ with possibly redundant states, as the NFA $N$ is not minimized. But ...
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334
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What is a regular expression for solutions to the dog/cat/mouse river crossing puzzle?
This is a question that's been bugging me off and on for years, ever since I took a compiler theory class as an undergraduate. There, we learned how to convert a regular expression into a non-...
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How many states in a 2 delay (or n delay) transducer (using DFA)?
An n delay transducer in the context of the problem simply means that the output is same as the input but after waiting for 2 more symbols in the input.
2-delay transducer: We can't show any result ...
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Expressing classic automata in modern terms
This semester I was introduced to finite automata (FSM), then pushdown automata (PDA), and now the Turing machine (TM). Granted that there're many possible implementations of these abstractions (...
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How does a minimal DFA ensure minimal computational cost?
I just went to read wikipedia to check a point on FA minimization, and
I read there the following sentence:
The minimal DFA ensures minimal computational cost for tasks such as
pattern matching.
...
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2
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When is the best time to include an ε-transitions in a NFA state diagram?
While doing my NFA homework in my automata class, I feel like I'm not taking advantage of the ε-transitions I'm learning about. I can solve problems without using it. It's not like I really need it, ...
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Convert a dfa to rule for a asterisk case
Here is a simple but very common grammar rule case in EBNF format, the Statements is a none terminal symbol and Statement is ...
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1
answer
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DFA for even concatenation of strings from a language
If I have a deterministic finite automaton (DFA) with a language $W$, and I need to create another DFA that returns all the strings that are a concatenation of an even number of strings in $W$, how ...
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Does graph traversal require stack machine?
I'm writing a graph traversal function to be used in a garbage collector.
To avoid stack overflow, I used a finite state machine. Roughly, it descends into child nodes recursively to mark objects, and ...
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1
answer
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Does there exist terminology to discern NFA states and NFA-transformed-into-DFA state?
I can't find this from surface search in the literature
When one observes/simulates NFA after processing several characters, one has to consider both "internal states of NFA" (individual ...
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Regex to DFA - How do I implement parsing preferences in regex search?
I've tried a to implement a Regex to DFA converter, and it works, so far, but I don't understand how to implement "parsing preferences" in the DFA.
A classic example is $a^*$. This regex is ...
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vote
2
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Need to create CFG that requires sum of other letters
I have a homework assignment that requires me to create CFG $G$ for
$$L = \{a^i b^{i+j+k} c^j d^k\}$$
so that it can accept words like ab, aaabbbbd, abbbcd, but it should not accept abba, aabbbbbc, or ...
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Is there an algorithm for generating non comparable boolean vectors?
First some context:
A Boolean Network of $n$ components is a function $f$ from the set $\{0,1\}^n$ (set of vectors of $n$ components whose values are 0 or 1) to itself.
The dynamical behavior of a ...
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Finite-state transducer to accept $i$'th word of DFA
If I have a DFA $D$ that accepts some regular language $L$, is it possible to construct some finite-state transducer $T$ that takes in an index $i$, and puts out the $i$'th word in $L$, ordered ...
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Design a two-tape deterministic Turing machine M that recognizes the language L3= {x#(0^k) #y : x, y ∈ {0, 1}* , x = y ∧ |x| = k}
I'm having a hard time trying to write a two tape Turing machine
I wanted to first think Oh all I'd have to do is scan from left-to-right till I find the strings that matches the accepted strings) ...
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0
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conversion of epsilon NFA to NFA
I was given below task:
Eliminate Epsilon-transitions in below automata
My solution:
Is it correct that stage 1 is actually one of the final stages?
How does it work in given example? We have ...
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49
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What if have a algorithm that could generate a NFA of 42 states of any binary string of 2^32 length?
For example, if we have a true algorithm that could generate any NFA of at most 42 states from any binary string of 2^32 length. So, this algorithm can not just recognize the string but just recreate ...
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Has anyone seen the following string classifier discussed?
The closes related question I have found for this is Find string patterns preferably in regex for string streams, but it has no answer and is also a little less constrained as my idea.
Given a set of ...
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0
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What is the connection between finite automata and logic (sequential calculus)?
Languages recognized by finite automata are exactly those definable
by sentences of the sequential calculus, and also exactly those
definable by rational expressions (also called regular expressions)
...
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How to prove existance and construct finite-state transducer between two different FSM?
For example I have 2 simple FSM. I will use regular expression for clarity.
...
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2
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Is my regular expression and finite automata diagram for this state table correct?
So i have some theory of computer science homework and I'm struggling with this question currently. I am given the following automaton:
$Q = \{q_0,q_1\}$.
$\Sigma = \{a,b\}$.
$q_0 = q_0$.
$F = \{q_0\}...
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1
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How to efficiently flatten a hierarchical state machine?
David Harel's StateCharts introduces hierarchical states and history mechanism, which are really powerful when modeling complex system behaviour. But when doing model based testing we need a "...
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Draw a CFG (context-free-grammar) that starts and ends with the same symbol yet has odd number of 1's
I figured out that the CFG that starts and ends with the same symbol in alphabet $\Sigma=\{0,1\}$ will be :
S -> 0A0|1A1|0|1|
A -> 0A|1A|𝜖
How can i interpret the odd number of 1's also?
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0
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How design a Deterministic finite automata which accept string starting with 101 and how to draw transition table for it if there is a dead state
I’m trying to design a DFA
which accept string starting with 101 if the string start with 0 then it goes to dead state.Is my design is correct or wrong? And I don’t know how to draw transition table ...
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